Understanding Work, Power, and Energy in Physics
SUBJECT: WORK – POWER – ENERGY
Working Concept
In everyday life, the term work applies to any kind of activity that requires an effort, whether of intellectual or muscular origin. Thus, lifting a body, varnishing furniture, building a bridge or a building, planning a reform of any kind, writing a book, etc. are examples of activities where people work. However, in physics, the concept of work is used in a much more restricted sense. We say that mechanical work is performed upon the displacement of a force along its own line of action. This concept of work entails, then, as necessary, the following conditions:
- a) a defeated force, and
- b) a shift along this line of action
Therefore, there will be no mechanical work when either of these two factors is zero or absent. How do these factors influence the work? If we lift a body at some point we will have to overcome its weight by making a particular job. Clearly, if the height is doubled or tripled, the work carried out will also double or triple. That is: the work done to overcome a given force is directly proportional to the displacement experienced over its course of action. Moreover, if we lift a body double or triple the previous weight, at the same height, the work done will also double or triple. Then: The work done to overcome a force in a certain way along its course of action is directly proportional to the intensity of the defeated force.
Work = force overcome × displacement
If we call T to work, the force F, and displacement d, then we have the following formula for measuring work:
Equation.
That is:
The mechanical work done by a force to move a body is obtained by multiplying the displacement by the force component in the direction of travel.
Working and Applied Force
However, to overcome a force it is necessary to apply another in the opposite direction, so that every time you move a body we do apply a counterforce to those who oppose the motion. This applied force is not always in the direction of travel. Suppose, then, a body that moves horizontally under the action of a force F, at an angle to the direction of travel. The force F is decomposed into two parts: F1, in the direction of displacement, and F2, perpendicular to it. F1 tends to drag the body horizontally and F2 to lift it vertically. As F2 is canceled by the body weight, only F1 does work.
Therefore:
Equation.
cos that is a factor indicating how F1 varies in relation to the angle a and whose value is less than or equal to 1. Therefore, the mechanical work is given by:
Equation.
Of the different values of cos, we are interested in the following two:
1) Cos a = 1
The cos factor has the maximum value 1 when a equals zero, i.e., when the force F and displacement have the same direction. In this case the previous relation reduces to T = F × d in which the applied force is equal to the force module up, but in reverse.
2) Cos a = 0
The cos factor is zero when a is 90°, i.e., when the force F and displacement are perpendicular. But if cos a = 0, then the work done is zero. This means that no work is required to move the point of application of a force perpendicular to it.
Labor in a Gravitational Field
If a body is free in a gravitational field of the field’s own forces accelerate it toward the center of gravity for, so they do the work of moving the body. Then no need for external work to move a body within the meaning and direction of the respective field. On the contrary, to move in the opposite direction is a need for an external work against the weight, which is against the forces of the field. This is what happens when we raise a body vertically, the work done is T = P × h where h is the corresponding height. If you move the body between two points in the field with equal intensity, the work is zero, since in this case the body has not changed its distance from the center of gravity and therefore has only moved perpendicular to the direction of field strengths. It is the case of a body that moves in a horizontal plane: no work is performed to overcome its weight, but only to overcome friction.
Units of Work
In general, according to the formula, a unit of work is obtained by multiplying a unit of force per unit length. In the SI system the unit is called the joule.
1 joule = 1 newton x 1 m
A joule is the work done by force of 1 Newton to move its point of application at 1 m in the same direction of force.
Concept of Power
In the working definition, is outside the concept of time. In practice, the work is done by machines or engines that are characterized by a greater or lesser amount of work that may develop in a given time, that is, by its power. Power of a machine or engine is the work that is able to perform per unit time. That is:
Equation.
In practice it is common to express the power as the work performed in a second, i.e., it is regarded as the speed with which a particular job is done.
Power Supplies
In general, a unit of power is obtained by dividing a unit of work by one time unit. In the SI system the unit is called a watt. 1 watt = 1 Equation.
One watt is the power of a machine that can do the job of 1 joule per second. Also used per kilowatt, which is a multiple of the watt.
1 kw = 1000 w
As this small unit, in practice it employs a multiple of it, called steam horse. Also used the power unit called English horsepower or horse power (hp). 1 HP = 735 W = 0.735 KW
1 hp = 746 W = 0.746 KW
Other Units
They are the watt-hour and the kilowatt-hour. One watt-hour is the work done in 1 hour for a 1-watt motor power. Since 1 watt = 1 joule / sec. and 1 hour = 3600 seconds, we have: 1 WH = 1 joule / s × 3600 s
1 WH = 3600 joules A kilowatt hour is the work done in 1 hour, an engine of 1 kW.
JCVB – Physics 2004
Since this engine does work in 1000 joule per second, the work done in 1 hour is:
1 kwh = 1000 joule / s × 3600 s
or 1 kWh = 3,600,000 joules
Problem 1: An electric motor up to 4410 N 30 m high by 30 segundos.Calcula its horsepower.
Power and Speed
It is also important to consider and measure the power output at a given time by a machine in motion. Let F be a continuous and constant force acting on a body in motion. If we consider a time interval D t, small enough to estimate instantaneous speed, and their journey D d, in that interval, then the work done by force F is:
T = F × D d
and the instantaneous power shall be:
Equation.
But the ratio Equation. represents the instantaneous velocity of the moving body. Then, the above relationship reduces to:
Equation.
Concept of Energy
In all cases where work is done, the body that performs it requires something that allowed it to have the strength. For example, when a car engine burns fuel to set in motion the vehicle that something that gives you the strength is in the fuel, but must burn to dispose of it. In that something is given the name of energy and therefore we can say that:
Energy of a body or system is its ability to perform mechanical work. In practice, we use the term energy commonly linked to another that allows us to characterize its source. Thus, when we talk about:
Equation.
We are pointing to various forms of energy associated with its source. So important is the presence of energy in nature, which can hardly be a phenomenon that has no direct or indirect involvement. And their connection with matter is so close that we can also add: the energy is just a different form of matter or of this behavior.
Anyway, the concept of energy is always working so closely bound to his measure is given precisely by the work you can do the body that possesses.
To make the measurement is necessary to consider the conditions under which lies the body, since these determine the factors in practice. Of the various cases that can arise consider the following, which are most characteristic:
a) Bodies in Motion: a missile, a vehicle, running water, moving air masses, etc. in this case the possibility of doing work depends critically on how fast you move the cuerpo.Así, a projectile penetrates more deeply the greater its speed air flow turns the blades of a windmill the faster the higher is its own speed. etc.
b) Bodies at some point: a lamp, a water tank, a plane flight, etc.. The capability for work, this time depends on the height to which is the body. This opportunity takes place when the body falls, due to increased speed is experiencing. Thus, water from a reservoir is able to drive turbines if it is dropped from a height that allows you to acquire the necessary speed to set it in motion.
c) deformed elastic bodies: a compressed or stretched spring, a rope coiled clock, a compressed gas, a drawn bow, and so on. In this case the possibility of doing work depends on the forces of elasticity, propelling the body to regain its normal shape or primitive. Thus, a drawn bow can shoot an arrow, the compressed air actuates the brake linings to expand to the vehicle stopping to pose these types of brakes, a rope clock starts to unwind slowly its mechanism, and so on.
d) Bodies fuels and explosives: petroleum and petroleum products, timber, coal, gunpowder, dynamite, etc.. In the case of fuels, the possibility of labor depends on the heat they produce, and the explosives, depends on the expansive force caused by the combustion of the respective material.
Forms of Mechanical Power
The energy comes in many forms in nature: mechanical energy, heat, electricity, light, etc.. The mechanical energy manifests itself in two forms: potential energy and kinetic energy or latent or active. A body has potential energy or latent, whether because of its position, shape, chemical composition, etc.., Is able to perform work. In the examples cited, a body at a certain height has potential energy due solely to the position it occupies. In this case we will discuss potential energy of position or gravitational potential energy. Deformed elastic bodies distinguish them as examples of potential energy and elastic energy stored in case of a fuel, as examples of potential energy due to its chemical composition.
Instead, a body in motion can do work because of their speed. To stop will require a force that will move along a path, doing work. In this case, we talk about kinetic energy or force. A body has kinetic energy if, because of their speed is able to perform work.
They have potential energy:
1. Bodies which lie off the ground or any reference level in a gravitational field.
2. The deformed elastic bodies (springs compressed or stretched, compressed gases, etc.).
3. The explosives
4. The fuels (wood, coal, oil, etc.).
5. Food (fuel for living things)
6. etc.
Have kinetic energy:
7. Falling bodies in a gravitational field
8. Springs compressed or stretched, to be released
9. Compressed gases, expanding
10. Explosives to be detonated
11. Fuels, when burned
12. Food to be digested
13. Electric currents
14. Streams
15. Winds
16. etc.
Measurement of the Gravitational Potential Energy
Suppose that a body of weight W falls vertically from a height h above the ground or for any benchmark.
A
P
h
B
To take up this point were necessary work T = P × h equivalent to the body is capable of falling back into the ground. This study assessed the gravitational potential energy of the body when it is at the height h. Then: E p = P × h
Measurement of Kinetic Energy
The kinetic energy is measured by the work required to inform a body of mass m and velocity v. On the body, initially at rest, we apply the force F, with which this takes the acceleration, such that F = m × a
Suppose that the force acting on the body in time t along a path d, who will travel with uniformly accelerated motion, thus:
Equation.
This formula shows that:
1. At equal speed, the kinetic energies of two or more bodies are directly proportional to the square of their respective speeds.
2. At equal mass, the kinetic energies of two or more bodies are directly proportional to the square of their respective speeds.
This means that if a body doubles its speed, its kinetic energy quadruples, if tripled its speed, Ec increases nine times, etc. ..
Let’s say, finally, that units which express the extent of mechanical energy are the same in the measurement work.
Principle of Conservation of Mechanical Energy
When a body rises vertically, its velocity decreases, gradually, until it becomes zero when it reaches its maximum height. This obviously implies a variation of the kinetic energy of the body, which is greatest at the starting point and zero at the highest point. But as the body rises, its potential energy will be increased gradually to peak when it reaches its height. This means that the kinetic energy is gradually transformed into potential energy when the body rises, and similarly, the potential energy becomes kinetic energy, the lower the body. This transformation is such that at any point in the trajectory of the body decreased Ec is equivalent to increasing Ep and vice versa. In other words, at any point of the trajectory we have:
Ec + Ep = constant
This simple example gives us a clear idea of what is the principle of conservation of energy, which can be stated as follows:
In an isolated system, the total mechanical energy remains constant.
An isolated system is one in which no energy exchange takes place with bodies outside the system. A system with this feature is called a conservative system.